3.22 Convert the coordinates of the following points Cartesian to cylindrical and spherical coordinates: * (a) P = (1, 2,0) (b) P2 (0,0, 2) (c) P3 = (1, 1,3) (d) Pa = (-2, 2, -2)

Q: Which of the following is the cylindrical coordinates of (–1, /3, –2)? O a. (2, 5,–2) O b. (4, 5,…

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Q: Convert from the Spherical Coordinate to the Cylindrical Coordinate AO 3 3 37 2 2'2 BO 3' 2 Co 3 3 3…

A: Conversion of spherical coordinates to cylindrical coordinates

Q: 5. a) Convert points P(1,3,5), T(0,–4,3), and S(-3,-4, –10) from Cartesian to cylindrical and…

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Q: 1) Use spherical coordinates to evaluate 4-x² -y² 4-x2-y2 4-y² LaSNa- y²/x² + y² + z² dzdxdy

A: The given problem is to evaluate the given triple integral using spherical coordinates, We have to…

Q: 3. Given the function, W=x²+y²-z?, using spherical coordinates equations, find the aw aw dw and дө

A: It is given that, w=x2+y2-z2 It is known, that cartesian coordinates can be written in spherical…

Q: Which of the following is the rectangular coordinates of the point which is given by cylindrical…

A: Cylindrical (ρ,θ,z) to cartesian (x,y,z) conversion formula is -: x = ρ × cosθ  y = ρ × sinθ  z = z…

Q: Which of the following is the cylindrical coordinates of (-1,-V3,2)? Oa (4, 품, 2) O b. (2, 5,2) O…

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Q: 4-x² –y² b.) z dz dy dx -VI¬x² J /3x²+3y? from Cartesian coordinates to spherical coordinates.

A: We need to find the geometry of the given integral.  Then find the limits in terms of spherical…

Q: 5. Use spherical coordinates to evaluate /16--2² Not √16¬x² / √x² +yª √x² + y² + z² dz dy dr.

A: The given problem is to evaluate the given triple integral by converting the Cartesian coordinates…

Q: sketch the solid whose spherical coordi- nates (p, 4, 0) satisfy the given inequalities. 0<p<2/cos…

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Q: 6. By converting to spherical coordinates, evaluate 22 dz dx dy. 0.

A: triple integral

Q: Convert the point (x, y, z) = (– 4, 2, 5) to spherical coordinates. Give answers as positive values,…

A: We are asked to convert  to spherical coordinates.

Q: (a) Express the following points in cylindrical and spherical coordinates: (i) P(1, -4, -3); and…

A: We need to find cylindrical and spherical coordinates.

Q: Which of the following is the cylindrical coordinates of (-1, 3,-2)? Oa (2, 즐,-2) O b. (2, ,-2)…

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Q: In three dimensions, the cylinder x? + z2 – 10x – 6z – 2 = 0 has radius k i +tj+ and the axis line…

A: Radius =6  r(t)= (5+6cos(thetha))i+tj+(3+6sin(thetha)k

Q: Which of the following is the cylindrical coordinates of (-1, -/3,2)? O a. (2, 품, 2) O b.(2, – 5, –…

A: Explanation of the answer is as follows

Q: 2. Convert the following from Spherical Coordinates to Cylindrical and Cartesian Coordinates: (b)…

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Q: Find an equation of the form p = f (0, $) in spherical coordinates for the surfac z = 8

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Q: Use spherical coordinates. Evaluate |/| (x2 + y²) dv, where E lies between the spheres x2 + y2 + z2…

A: For spherical coordinates: x = ρ sinφ cosθ, y = ρ sinφ sinθ z = ρ cosφ. So,       x2+y2=ρ sinφ…

Q: 9. Show that for a ± 0, the equation p = 2a sino cos 0 in spherical coordinates describes a sphere…

A: Given :  The equation ρ = 2 a sin ϕ  cosθ  .   To determine: The equation ρ = 2 a sin ϕ  cosθ  in…

Q: find an equation of the form ρ = f (θ , φ) in spherical coordinates for the following surfaces  x2…

A: Solution:- x2-y2=4 x=ρ sinφ cosθ y=ρ sinφ sinθ   ρ sinφ cosθ2-ρ sinφ sinθ2=4 ρ2 sin2φ cos2θ-ρ2 sin2φ…

Q: Express the following points in cylindrical and spherical coordinates: (а) Р(1, — 4, — 3) | (b) Q(3,…

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Q: 5. Use spherical coordinates to evaluate r2+ y2 +22 dz dy dr. 16-

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Q: 1. Sketch carefully the solid enclosed by the three cylinders x + y* – 1,x² + 2² = 1, and y + z² =…

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Q: 4-22-y2 Compute y? Vx2 +y? + z² dz dx dy by converting to spherical 4-x2- coordinates.

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Q: 1) Use spherical coordinates to evaluate 4-y² c4-x²-y² 4-x2-y2 Li L y²/x² + y² + z² dzdxdy

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Q: (a) Express the following points in cylindrical and spherical coordinates: (i) P(l, -4, -3); and…

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Q: Which of the following is the rectangular coordinates of the point which is given by cylindrical…

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Q: Evaluate the spherical coordinate integ A1 8 sin o | ? sin d dp dɖp de do de 0 0 512 2 O A. -

A: Here we have to calculate I= ∫0π∫0π∫08 sinϕ ρ2 sinϕ dρ dϕ dθ

Q: *3.22 Convert the coordinates of the following points Cartesian to cylindrical and spherical…

A: As per Bartleby's answering policy, we can answer only one question with a maximum of three subparts…

Q: 1) Converting Cartesian to spherical x +y + (z - 1)? = 1

A: The relationship between cartesian and spherical coordinates are :

Q: Which of the following is the cylindrical coordinates of (-1, 3, -2)? O a. (2, 플, 2) O b. (4, 품,-2)…

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Q: Which of the following is the cylindrical coordinates of (-1, –/3,2)? O a. (4, 품, 2) O b. (2, 플, 2)…

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Q: Which one of the following assumptions is known as the spherical disturbance assumption? E(uu') = 2…

A: Let us consider a linear regression model : Here we have the disturbance term, ε=u Whether a…

Q: 3. Use spherical coordinates to valuate ff, y? dV where E is enclosed by the hemisphere x? + y? + z?…

A: Given that  ∫∫∫Ey2dV and  enclosed by the hemisphere, x2+y2+z2≤9,y≥0 Here to evaluate the integral,…

Q: (b) To change from spherical coordinates to Cartesian coordinates we use the equations x =r cos 0, y…

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Q: 9. Convert from cylindrical to spherical coordinates (a) ( /3 , t/6, 3) (b) (1, t/4, -1) (c) (2,…

A: According to our guidelines, In case of questions with multiple subparts we are supposed to answer…

Q: Given the point D(−4, 5, 3) and A = yax + (x + z)z ay, express the D and A in: Kindly answer in…

A: D=(-4, 5, 3)Vector A=y ax +(x+z)z  ay +0  azρ=x2+y2  =(-4)2+(5)2ρ=41ϕ=tan-1yx…

Q: 5. Use spherical coordinates to evaluate [[[ (x² + y² + 2²) ² dv D where D is the solid hemisphere…

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Q: (b) Use spherical coordinates to evaluate l y²dV_where E is the solid hemisphere a? +y² + z² 0. E

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Q: Which of the following is the rectangular coordinates of the point which is given by cylindrical…

A: Cylindrical to rectangular transformation is made by following rule,

Q: Which of the following is the cylindrical coordinates of (-1, y/3, –2)? O a. (2, 플, -2) O b. (2, 폭,…

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Q: 4. Consider the circular helix given by 7(t) = (3 cos t, 3 sin t,4t). Give an equation for the…

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Q: Which of the following is the rectangular coordinates of the point which is given by cylindrical…

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Q: Which of the following is the cylindrical coordinates of (-1, -/3,2)?

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Q: 5. Use spherical coordinates to evaluate LIVE √√= ²+ y² + 2² dz dy dr.

A: Given ∫-44∫-16-x216-x2∫x2+y24x2+y2+z2 dzdydx

Q: 1-For spherical polar coordinate system Zr Zr (2² exp(- 2a 1 Z. -) sin OCosø 42 `a а Jy„V„dV = 8_ =?…

A: For spherical polar co-ordinate system ψpx=142Za32exp-Zr2aZrasinθcosϕTo find:∫ψpxψpxdV=δxx

Q: 12. Find the distance from the point P(0,0,0) to the plane given by x + y +z= 6.

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